Questions about models for the valuation of option contracts.

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Open source code based on quandl for security analysis and options priming

Quandl seems to be an excellent source of wide range of free/open financial data. But is there an open source code or platform that uses the quandl datasets to perform security analysis and option ...
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30 views

Generating process for stock price paths in this paper?

I am reading Longstaff and Schwartz Valuing Aerican Options by Simulation because monte carlo simulations, especially their use in option pricing, is interesting to me. However, I am having some ...
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Replicant portfolio with commissions (Jarrow Rudd)

I have created a Jarrow Rudd three for a call option that I know how to replicate with a portfolio. A replicating portfolio of a option works this way: At time 0 we form a replicating portfolio ...
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31 views

Stochastic volatility and forward start contracts

Why is it more accurate to use stochastic volatility when pricing let's say a forward start option (ie an option priced today but striked in a future date) ?
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2answers
101 views

Accuracy Rebonato Swaption Approximation Formula among Different Strikes

Can somebody explain me if the Rebonato swaption volatility approximation formula is accurate for only ATM strikes, and if yes why? Can it also be used for ITM and OTM strikes? My foundings: Let $0 &...
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76 views

Problems with a Black-Scholes modified equation

I haven't really studied much financial mathematics until about 2 months ago so I'm quite new to this stuff, so I'm sorry if this is a trivial question. At the moment I'm trying to work out what the ...
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44 views

Overpricing Bermudan swaption using Shifted LMM

I am trying to model a callable range accrual note linked to the EUR CMS spread, 20Y-10Y, with cap and floor. The note is Bermudan, callable starting year 3, every 3 years till maturity at 30 year. We ...
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1answer
67 views

shifted SABR - ATM vol

quick question guys. I know that for Shifted SABR (or any other Shifted model), we simply model the underlying price process (lets say the forward interest rate F), as F' = F + x, x being the shift. ...
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81 views

What are the answers to these questions on card deck and option pricing?

here are 3 questions I have some trouble dealing with. Your help will be greatly appreciated! 1 - We have a deck card: 26 red, 26 black. we play a game: you draw a card from the deck without putting ...
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1answer
65 views

Isn't Black's approximation for American options inconsistent?

I have came across a formula suggested by Fisher Black (Fact and fantasy in the use of options, FAJ, July–August 1975, pp.36) for approximating the price of an American call written on a dividend-...
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80 views

Applying Black-Scholes to valuing index options

I am currently attempting to use the Black-Scholes model to value index options. My issue is; what should I use as the price of the underlying? Say I want to value a call option on the German DAX with ...
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90 views

Why is the value of an adaptive stochastic process known at time t?

I am having a hard time to understand the concept of an adapted stochastic process. Using an analogy to finance, I have been told we can think of adaptiveness of a stock price process as having an ...
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72 views

Qualitative properties of call

I have read somewhere that we can show by using arbitrage argument the following relationship for call option : $$\frac{\partial{C_t(T,K)}}{\partial{K}}\leq0$$ $$\frac{\partial^2{C_t(T,K)}}{\...
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2answers
119 views

Solution for american perpetual put

I have been attempting an exercise in which I have to determine the value of an american perpetual put, $P$ in terms of the asset value $S$. The solution to the exercise says: When $S>S_f$ (the ...
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78 views

Butterfly spread model price

Consider a butterfly spread with strikes $K_1, K_2, K_3$. My professor wrote the model price, $V$, was equal to the following: $$V = exp(-rT) * P(K_1<S_T<K_3) * (1/2) \Delta K$$ where $\Delta K ...
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180 views

How to calculate Implied Volatility for out-of-the-money options?

I'm trying to calculate the implied volatility for out-of-the-money options, and to a lesser extent, in-the-money options. Most of the literature estimations I could find for implied volatility were ...
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1answer
74 views

Arbitrage opportunity in discrete time

Say we have the following binary option $B$ on asset $S$ with strike K and expiration time T, assume also that the following relation holds at time $0$: $B > N*C(K,T)-N*C(K+1/N,T)$ Where $N$ is ...
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3answers
84 views

Distribution of pay-off of an exotic option

Can any assumptions be made about the pay-off of an exotic option? For example, might we say the distribution of the pay-off a vanilla option would be Normal? I have built a valuation tool that ...
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47 views

Capital increase: which stock price to use as input to Black-Scholes formula?

For an exercise we have to calculate the theoretical value of a scrip / preferential right on its issue day (23 April) in the context of a capital increase. The scrips are issued on 23 April. The ...
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173 views

How do different models impact option Greeks?

If I trade an option using delta, vega, Prob OTM, etc. these are derived from a model. How do leading models impact valuations in terms of the Greeks? I suppose to form a baseline it would have to be ...
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2answers
80 views

Counting random paths

Assume the path of a certain stock can be modeled using a binomial tree. The initial price of the stock at time $t=0$ is 1024. The upstage factor of the stock price is $x=1.25$ and downstage factor of ...
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57 views

Option pricing: Risk neutral probability calculation

Let $u=1.3$ $d=0.9$ $r=.05$ $S(0)=50, X = \text{strike} = 60$. Assume binomial model Why isn't the risk neutral probability found by solving the following for $p$: $$E[S(T)]=p65+(1-p)45=S(0)(1+r)^T=...
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93 views

Monte Carlo Option Pricing: Averaging Price Per Path

In Glasserman's book, he computes the price of an option by first computing the average price over each simulated price path. Once all the paths have been simulated, the average of all the payoffs is ...
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Proving the convexity of put price [duplicate]

Prove that the price of the European put option is a convex function of the strike price in one-step binomial model. In other words, if $P_E(X)$ is the price of the European put option in one-step ...
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46 views

Portfolio replication option pricing: Money market position

Why when replicating a call option, the money market position (bond, risk free investment) is negative and when replicating a call option, the money market position is positive? Please explain ...
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1answer
58 views

Put-on-call option confusion

So the question asks: Given a 3-steps Binomial Tree model with $S(0) = 50$, $U = 20%,D = 􀀀20%$, and $R = 5%$. A European call option has the strike price $X = 40$ and maturity time $T = 3$. Also, a ...
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44 views

Put call parity: when are the premiums the same?

Please explain why put call parity could be compared to the payoff of a long forward contract. ie. $C_E-P_E=V_X(0)$ where $C_E,P_E$ are the call/put premiums and $V_X(0)$ is the value of a long ...
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83 views

Replication strategy of European call option

So the question asks: L et $S(0) = 120$ dollars, $u = 0.2$, $d = −0.1$ and $r = 0.1$. Consider a call option with strike price $X = 120$ dollars and exercise time $T = 2$. Find the option price and ...
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34 views

Connecting Call price computed discretely to call price computed under continuous time case

I want to connect the call premiums calculated discretely via the binomial pricing method to the Black-Scholes-Merton formula for the call premium which applies to continuous time case. The framework ...
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3answers
98 views

Construct option and stock portfolio

If a riskless security costs 100 today and will cost 120 at time T, a stock costs 50 today and will either be 70 or 30 at time T, and call options on the stock have strike price 50 expiring at time T, ...
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223 views

The Upper Bound of an American Put Option

I have just read the following paragraph (in bold) and have a question on the upper bound of an american put option: http://www.sharemarketschool.com/option-valuation-upper-and-lower-bounds-part-...
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5answers
391 views

Estimate probability of limit order execution over a large time frame

I have a negligible amount of money (\$5000) that I would like to invest in a stock. I would like to buy the stock at some point in the next year, and get the lowest possible price. I would like to ...
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2answers
165 views

Why is the term structure of the implied volatility surface non-monotonic?

Does this reflect expectations & uncertainty about interest rates (exposure to rho?), event driven concerns about the underlying, or something else?
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59 views

Binary American Call Option (Cash or Nothing)

Suppose we have a stock with current price $S(0)=X$ and the interest rate is zero. When the stock reaches level $\$ H$ for the first time ($H>X$), the option can be exercised and its payoff is $\$ ...
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81 views

Linear combination of payoffs of bull and bear spreads

Write the following payoffs as linear combination of call options with different strikes and possibly some cash and give the closed form formula for them. Attempted solution: The payoff for the bear ...
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112 views

Why are there two expressions for the Black-Scholes hedging portfolio

I am new to derivatives pricing and am trying to understand why there are two different expressions for the Black-Scholes hedging portfolio. The first approach, used in books like Hull, stipulates ...
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1answer
58 views

A clarification on the Heston option pricing formula

I have carefully reconstructed all the computations that lead to the Heston option pricing formula for a call. I end up with this formula for the "adjusted" probabilities $$ P_j\left(x,v,T;\ln K\...
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1answer
36 views

Known future volatility and difficulty in predicting final P/L

I have started Chapter 1 of Dynamic Hedging by Taleb and it starts by saying "Even if traders knew the exact future volatility but hedged themselves (rebalanced the gamma) at discretely spaced ...
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Pricing function $P(S,t)$ is convex in $S$ for all $t$

I am now reading Alternative Characterization of American Put Options by Carr et all (available at http://www.math.nyu.edu/research/carrp/papers/pdf/amerput7.pdf). There is a theorem called 'Main ...
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1answer
85 views

Lookback option to find stock price

Consider the payoff equation for the lookback option $\psi(T)= max(S_t-S_T)$, where $t\in[0,T]$ and $S_t$ is modeled by the geometric Brownian motion with constant parameters. Find the price of stock ...
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53 views

Potential Arbitrage profit or proof problem

So the question asks: Consider 4 following European call and put options with the same maturity time: Call option with strike price $100$ sell for $45$ Call option with strike price $110$ sell for $...
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56 views

Interpolating on the BS parameters and injecting in the BS formula vs interpolating directly on option prices

Let's consider a simple European call option. In practice, the way the Black-Scholes formula is used to price it is by injecting all of the parameters and paying special attention to the volatility ...
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Euler discretization bias, heston model

I am performing option pricing using Heston model and Euler discretization. I'm getting the following result: ...
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78 views

recent developments in American options?

I have read the paper written by Egloff (2005) using machine learning techniques to solve the optimal stopping problem. Is there any development in pricing American options during 2005-2016? (based ...
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3answers
139 views

Binary Option in B-S model - technical question

I want to price Binary Option in Black-Scholes model. The payoff is of the form $f(S_{T})=I_{\{S_{T}-K>0\}}$. If we assume that $t=0$ this is easy, because then we have $C_{0}=\mathbb{E}^{*}\...
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100 views

Why is $N(d_2)$ not needed for hedging?

I'm trying to understand delta hedging. If I sell a plain vanilla call option, in order to delta hedge it, I have to buy delta amount of stocks. What I don't understand is that the BS price of the ...
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153 views

How to use the Black-Scholes formula with LIBOR rates?

I want to price an FX option using the Black-Scholes model, but I don't know the risk free rate, nor the volatility. I only know the LIBOR rates, the strike, and that the expiration day is 87 days ...
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64 views

How to price jumps in payoffs

I specifically want to know how to model a jump condition while valuing a derivative.Example :- the jumps which are observed in digital product payoffs, or barriers and knockouts. Although a ...
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100 views

Is complete market or not if appreciation rate is random?

Consider the stock price process satisfies the following SDE: $dS_t=\mu_t S_tdt + \sigma S_t dW_t , S_0=s $ and the appreciation rate process $\mu_t$ satisfies the following SDE: $d\mu_t=(a-\mu_t)...
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70 views

Payoff of a butterfly c++

I would like to price options (call, put,, butterfly) with monte-carlo method, but actually I need the expression of the butterflay payoff; Could you ^please help me !